The applicant of the application concerned has proposed a method for uniformly describing a tooth surface of a pair of gears in Japanese Patent Laid-Open Publication No. Hei 9-53702. That is, a method for describing a tooth surface, which can uniformly be used in various situations including for a pair of parallel axes gears, which is the most widely used configuration, and a pair of gears whose axes do not intersect and are not parallel with each other (skew position), has been shown. Furthermore, it has been shown that, in power transmission gearing, it is necessary that the path of contact of the tooth surfaces should be a straight line in order to reduce a fluctuation of a load applied to bearings supporting shafts of gears. In addition, it has been clarified that a configuration wherein at least one tooth surface is an involute helicoid and the other tooth surface is a conjugate surface satisfies the condition that a path of contact of the tooth surfaces should be a straight line. In the case of parallel axes gears, such as spur gears, helical gears, this conclusion is identical with a conclusion of a conventional design method.
Furthermore, conventional gear design methods for non-parallel axes gears have been empirically obtained.
In the case of non-parallel axes gears, it has not yet been clarified that there actually exists a pair of gears wherein one gear has an involute helicoidal tooth surface and the other gear has a conjugate tooth surface for the involute helicoidal tooth surface and, further, an efficient method for obtaining such a pair of tooth surfaces was unknown.